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Mindful of the optics of an all-male panel grilling an alleged sexual-assault victim, Republicans on the Senate Judiciary Committee have begun narrowing their search for an outside counsel to question Supreme Court nominee Brett Kavanaugh’s accuser this week.

One name in particular appears to be garnering support among committee Republicans: their onetime colleague, former Sen. Kelly Ayotte (R-NH).

Two Republican Senate sources confirmed to The Daily Beast that Ayotte is being considered as a potential candidate to question Christine Blasey Ford, who has accused Kavanaugh of sexually assaulting her at a high-school house party in the early 1980s. Ford is slated to recount her allegations on Thursday, pending negotiations with committee leadership on the particulars of her testimony.

A top Democratic Senate source also relayed hearing that Ayotte’s name was under consideration, though a GOP aide on the judiciary committee cautioned that the ex-senator had not been on their list as of last week. That aide said the list may have changed, that no decision had been made yet, and that numerous other women were also under consideration.

Playing the role of outside counsel would be a natural fit for Ayotte. The one-term senator, who lost her re-election bid in 2016, formerly served as the attorney general of New Hampshire from 2004 to 2009. She also has experience with Supreme Court confirmation fights, having shepherded Justice Neil Gorsuch’s nomination through the upper chamber last year.

For Senate Republicans determined to avoid the politically problematic visuals of a panel of older and middle-age men interrogating an alleged sexual-assault victim, Ayotte has the added benefit of a being a woman.

It’s not clear that Ayotte would accept the gig if it were offered to her, or even that an offer will materialize. Some sources who spoke with The Daily Beast said it would be both a difficult and politically fraught role for the former senator, and could raise concerns about impartiality given that she was only recently an elected official of the party attempting to force a vote on Kavanaugh’s nomination.

“[S]he’d be crazy to take that job,” one Democratic staffer working on the nomination fight told The Daily Beast on Monday.

A source in the trenches on the pro-Kavanaugh side, who also said Ayotte’s name has been mentioned, said the ex-senator would be a strong choice, but would also raise some questions about impartiality. “There are a lot of pluses to her. She is sharp and talented,” said the source, who is familiar with, but not directly involved in, the search for an outside counsel. “But she is a former senator, so not sure how that works."

Senate Majority Leader Mitch McConnell’s (R-KY) office referred questions on the matter to the judiciary committee. A spokesman for the Republican side of the judiciary committee did not immediately respond to a request for comment. A White House spokesperson also did not respond.

Ford’s attorneys and Senate Democrats have argued that only senators should be allowed to question Ford, under the belief that GOP lawmakers should have to stand by their skepticism of her account.

“If my Republican colleagues don’t think that they can handle the challenge of respecting Dr. Ford, of questioning her in an appropriate and supportive way, then perhaps they shouldn’t be serving on the committee,” Sen. Chris Coons (D-DE), a member of the committee, said Sunday night on MSNBC.

But Republicans on the committee have rejected that demand, dubbing it a political ploy.

“Democrats have jumped on that too, probably because if senators aren’t asking questions, they won’t be able to talk about Anita Hill quite as much,” one aide to a senior committee Republican told The Daily Beast over the weekend, referring to the woman to accused Clarence Thomas of sexual harassment in 1991.

It was one of the key sticking points as both sides were negotiating the terms of Ford’s testimony last week, but Ford’s legal team eventually agreed to the Thursday hearing without assurances on the issue of an outside counsel.

Democrats, meanwhile, plan to lean heavily on two senators in particular during the hearing, Sens. Amy Klobuchar (D-MN) and Kamala Harris (D-CA). Both are former prosecutors who have dealt with sex-crime cases.